Dec

31

The idea of triangular congruency possessing basic reductionist strength is apparent in nature, social interaction and by extension, market behaviour and transactions.

One market relationship which exhibits this property is the classic triangular currency arbitrage, which allows for the determination of the equilibrium cross-rates of three currencies. This necessarily invokes that most central tenet in arbitrage theories, the Law of One Price. And interestingly, some definitions have the Law of One Price as: "the resting place for an asset's price and arbitrage is the action that draws prices to that spot. The absence of arbitrage opportunities is consistent with equilibrium prices, wherein supply and demand is equal". Again this invariably leads back to the idea of a triangulated relationship between the two sides of demand and supply engaging to arbitrage/converge a plumb-line to the base of the equilibrium state/price.

The essential question in the financial markets of course, is in determining just how individual agents/traders’ market views (normally differing on many levels) transform or align into a herding market sentiment. Some interesting studies have used the percolation model (from the physical sciences) in accounting for how market views spread through a financial network topology; the crux lying in how network feedback builds and eventually escalates past the percolation threshold i.e. reaches criticality. A simple treatment utilizes a two-dimensional lattice of individual agent/trader interacting and inter-influencing neighbouring sites - reducing it to a pure geometrical percolation problem. And here the common triangular lattice is used as the basic building block for the network topology.